Local Planning: The Dynamic Window Approach

A local planner decides what to do in the next fraction of a second. The dynamic window approach only considers speeds the robot can actually reach given its acceleration limits. For each candidate, it simulates a short arc, throws out the ones that would hit something, and scores the rest on heading toward the goal, distance from obstacles, and speed.

Weight: head toward the goal Weight: stay clear of obstacles Weight: go fast Obstacles move

The dynamic window

Given the current speed $v$ and turn rate $\omega$, the reachable window over the next control step $\Delta t$ is limited by the accelerations:

$$V_d = \big[v - \dot v_{\max}\Delta t,\ v + \dot v_{\max}\Delta t\big] \times \big[\omega - \dot\omega_{\max}\Delta t,\ \omega + \dot\omega_{\max}\Delta t\big]$$

Each sampled $(v, \omega)$ in that window is rolled out for a short time and scored, with colliding rollouts discarded:

$$G(v, \omega) = \alpha\,\text{heading} + \beta\,\text{clearance} + \gamma\,\text{speed}$$

What to notice

Red rollouts would collide and are never chosen. With a high clearance weight the robot keeps a wide berth but can stall in tight spaces. With a high speed weight it moves boldly and cuts close. Because it only looks a moment ahead, DWA can be trapped by obstacles shaped like a U, which is why it runs under a global planner. Nav2's DWB controller is a modern version of this idea.